Find the value of x.

The area of the smaller triangle is 12 square units

If the scale factor between two similar triangles is 2/3

It means that every length of the smaller triangle is 2/3 the length of the corresponding side of the larger triangle.

So, the ratio of their areas is the square of the scale factor

This is represented as

(area of smaller triangle) / (area of larger triangle) = (2/3)^2 = 4/9

We are given that the area of the larger triangle is 27

So, we have

Area of smaller triangle/27 = 4/9

Multiplying both sides by 27, we get:

Area of smaller triangle = (4/9) * 27

Evaluate

Area of smaller triangle = 12

Hence, the area of the smaller triangle is 12.

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The equation for the trigonometric graph is y = 2sin4x

A trigonometric graph is the graph of a trigonometric function.

Since we desire to find the equation of the graph, we then want to use the equation for the general sine graph.

y = AsinBx where

Now, A = (maximum - minimum)/2

From the graph,

So, we now substitute the variables into the equation, thus

A = (maximum - minimum)/2

= [2 - (-2)]/2

= (2 + 2)/2

= 4/2

= 2

Also B = 2π/T

Now from the graph, T = π/2

So,  we substitute for B in the equation for B, thus

B = 2π/T

= 2π/(π/2)

= 2π × 2/π

= 4

We then substitute A and B into y, thus

y = AsinBx

= 2sin4x

So, y = 2sin4x

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According to the given information, the slope of line AB is  [tex]\frac{2}{3}[/tex].

What is the slope?

The slope of a line is a measure of how steep the line is. It tells us how much the y-coordinate of the line changes for each unit of change in the x-coordinate.

To visualize a slope, imagine a line on a coordinate plane. If the line is steep, it means that for each unit of increase in the x-coordinate, the y-coordinate changes by a larger amount. Conversely, if the line is less steep, it means that for each unit of increase in the x-coordinate, the y-coordinate changes by a smaller amount.

To find the slope of a line that passes through two given points, we use the slope formula:

[tex]slope = \frac{(change in y) }{(change in x)}[/tex]

In this case, we have points A(0, -2) and B(3, 0).

So the change in y is 0 - (-2) = 2, and the change in x is 3 - 0 = 3.

Therefore, the slope of line AB is:

[tex]slope = \frac{(change in y) }{(change in x)} = \frac{2}{3}[/tex]

Since the slope is positive, we know that the line slants upwards as we move from left to right on the coordinate plane.

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The measure of the angle M is 129 degrees

It is important to note that the properties of a parallelogram are;

Then, we have that;

m< M = m < K

substitute the values

12x - 39 = 8x + 17

collect the like terms, we have;

12x - 8x = 17 + 39

Add the collected like terms, we get;

4x = 56

divide both sides by the coefficient of 4, we get;

4x/4 = 56/4

Divide the values

14

Then, m < M = 12(14) -39 = 129 degrees

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The complete question:

In the parallelogram, Find mZN: K (8x + 17)9 (12x - 39)8 01;0 - Lx'An M Ax+8x +17 + iax -3 = 360 3ax-33 = H0 +3 42 20 22X 7 x=17.30

The required surface area of the prism is 378 square meters.

To find the surface area of the prism, we need to know the dimensions of the prism. Let's call the length, width, and height of the prism l, w, and h, respectively.

Since the prism has right angles between its faces, we know that it is a right rectangular prism.

The formula for the volume of a right rectangular prism is V = lwh, and we know that the volume of the prism is 490m^3. Therefore,

lwh = 490

We are not given any specific values for l, w, or h, so we need to use another piece of information to solve for one of these variables.

The surface area of a right rectangular prism is given by the formula

SA = 2lw + 2lh + 2wh

If we can find the value of one of these dimensions, we can use it to calculate the surface area of the prism

lwh = 490

Since we know that the prism has right angles between its faces, we can assume that its dimensions are integers. We can start by testing integer values for l and w, and see if we can find an integer value for h that satisfies the equation.

For example, if we let l = 7 and w = 10, we get

7 * 10 * h = 490

Simplifying, we get

70h = 490

Dividing both sides by 70, we get

h = 7

Therefore, the dimensions of the prism are l = 7, w = 10, and h = 7.

To find the surface area, we can substitute these values into the formula for SA:

SA = 2lw + 2lh + 2wh

= 2(7)(10) + 2(7)(7) + 2(10)(7)

= 140 + 98 + 140

= 378

Therefore, the surface area of the prism is 378 square meters.

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Answer:

y - 3 = [tex]\frac{3}{4}[/tex] (x + 8)

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

given

4x + 3y = - 24 ( subtract 4x from both sides )

3y = - 4x - 24 ( divide through by 3 )

y = - [tex]\frac{4}{3}[/tex] x - 8 ← in slope- intercept form

with slope m = - [tex]\frac{4}{3}[/tex]

given a line with slope m then the equation of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-\frac{4}{3} }[/tex] = [tex]\frac{3}{4}[/tex]

-------------------------------------------

the equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b ) a point on the line

here m = [tex]\frac{3}{4}[/tex] and (a, b ) = (- 8, 3 ) , then

y - 3 = [tex]\frac{3}{4}[/tex] (x - (- 8) ) , that is

y - 3 = [tex]\frac{3}{4}[/tex] (x + 8) ← equation of perpendicular line

Answer:

Step-by-step explanation:

a. 25% of 5000 tickets = 0.25 x 5000 = 1250 tickets

Total sales of $45 tickets = 1250 x $45 = $56,250

b. 15% of 5000 tickets = 0.15 x 5000 = 750 tickets

Total sales of $35 tickets = 750 x $35 = $26,250

c. General admission tickets = Total tickets - Reserved tickets

= 5000 - 1250 - 750

= 3000 tickets

d. Total sales for general admission tickets = Number of general admission tickets x Price per ticket

= 3000 x $20

= $60,000

e. Total sales = Sales of $45 tickets + Sales of $35 tickets + Sales of general admission tickets

= $56,250 + $26,250 + $60,000

= $142,500

Answer:

the net asset value of Rae's antivirus software two years after her purchase was $570.84, which is not one of the given options.

Step-by-step explanation:

The software was used for 12 years, and Rae is selling it now. So, it has been used for 12 - 2 = 10 years.

Annual depreciation = (cost - salvage value) / useful life = (985 - 0) / 12 = 82.08

Depreciation for 10 years = 82.08 x 10 = $820.80

Net asset value after 2 years = cost - accumulated depreciation = 985 - 82.08 x 2 = $820.84

However, Rae is selling the software for $250, so her net asset value is $820.84 - $250 = $570.84

Therefore, the net asset value of Rae's antivirus software two years after her purchase was $570.84, which is not one of the given options.

Answer:

Mary Ellen is MOST LIKELY going to use shears to cut the linen.

Answer:

The end behavior of the given radical function f(x) = 4√(x-6) as x approaches positive infinity is option A: As x approaches positive infinity, f(x) approaches positive infinity.

Step-by-step explanation:

This is because as x approaches positive infinity, the value inside the square root (x-6) also approaches positive infinity. As the square root of a positive number is also positive, f(x) approaches positive infinity.

We can also see this by using the concept of limits. As x approaches positive infinity, the limit of f(x) can be evaluated as:

lim f(x) = lim 4√(x-6)

x→∞ x→∞

= 4√(lim(x-6))

x→∞

Since the limit of (x-6) as x approaches positive infinity is positive infinity, we have:

lim f(x) = 4√(∞) = ∞

x→∞

Therefore, as x approaches positive infinity, f(x) approaches positive infinity.

Answer:

Step-by-step explanation:

The end behavior of the given radical function f(x) = 4√(x-6) as x approaches positive infinity is option A: As x approaches positive infinity, f(x) approaches positive infinity.

This is because as x approaches positive infinity, the value inside the square root (x-6) also approaches positive infinity.
As the square root of a positive number is also positive, f(x) approaches positive infinity.

We can also see this by using the concept of limits.
As x approaches positive infinity, the limit of f(x) can be evaluated as:

lim f(x) = lim 4√(x-6)x→∞ x→∞= 4√(lim(x-6))x→∞.

Since the limit of (x-6) as x approaches positive infinity is positive infinity, we have:

lim f(x) = 4√(∞) = ∞x→∞.

Therefore, as x approaches positive infinity, f(x) approaches positive infinity.

To stretch the graph horizontally by a factor of 3, we need to multiply the x-coefficient by 1/3. Similarly, to stretch the graph vertically by a factor of 7, we need to multiply the y-coefficient by 1/7. Therefore:

Horizontally stretched graph: 5(1/3x)² + 8(1/3x) + 4y² - 4y = 70

Simplifying:

(5/9)x² + (8/3)x + 4y² - 4y = 70

Vertically stretched graph: 5x² + 8x + 4(1/7y)² - 4(1/7)y = 70

Simplifying:

5x² + 8x + (4/49)y² - (4/7)y = 70

Answer:

the probability that a child is excluded from all rides is 0.5000 (rounded to three decimal places).

Step-by-step explanation:

We can use the standard normal distribution to solve this problem. We first need to standardize the height requirements using the population mean and standard deviation.

a) To find the probability that a child can go on all rides, we need to find the probability of getting a height of at least 54 inches.

z-score = (54 - 53) / 4 = 0.25

Using a standard normal table or calculator, we find that the probability of getting a z-score of 0.25 or greater is 0.4013.

Therefore, the probability that a child can go on all rides is 0.4013 (rounded to three decimal places).

b) To find the probability that a child can participate in only mild and moderate rides, we need to find the probability of getting a height between 42 inches and 48 inches.

First, we find the z-scores for each height requirement:

z-score for 42 inches = (42 - 53) / 4 = -2.75

z-score for 48 inches = (48 - 53) / 4 = -1.25

Using a standard normal table or calculator, we find that the probability of getting a z-score between -2.75 and -1.25 is 0.2375.

Therefore, the probability that a child can participate in only mild and moderate rides is 0.2375 (rounded to three decimal places).

c) To find the probability that a child can only go on mild rides, we need to find the probability of getting a height of less than 42 inches.

z-score = (42 - 53) / 4 = -2.75

Using a standard normal table or calculator, we find that the probability of getting a z-score of -2.75 or less is 0.0030.

Therefore, the probability that a child can only go on mild rides is 0.0030 (rounded to three decimal places).

d) To find the probability that a child is excluded from all rides, we need to find the probability of getting a height less than 42 inches or greater than 54 inches.

First, we find the z-scores for each height requirement:

z-score for 42 inches = (42 - 53) / 4 = -2.75

z-score for 54 inches = (54 - 53) / 4 = 0.25

Using a standard normal table or calculator, we find that the probability of getting a z-score of less than -2.75 or greater than 0.25 is 0.0987 + 0.4013 = 0.5000.

Therefore, the probability that a child is excluded from all rides is 0.5000 (rounded to three decimal places).

An equation of a line parallel to that passes y = 4/3x + 4 through the point (3, -7) include the following: A. y + 7 = 4/3(x - 3).

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical expression:

y - y₁ = m(x - x₁)

Where:

Since y = 4x/3 + 4, the slope is equal to 4/3.

At data point (3, -7) and a slope of 4/3, a linear equation for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - (-7) = 4/3(x - 3)  

y + 7 = 4/3(x - 3)  

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By answering the presented question, we may conclude that As a result, equation the real circumference of the triangle space is around 30 metres.

A math equation is a technique that links two assertions and denotes equivalence using the equals sign (=). In algebra, an equation is a mathematical statement that proves the equality of two mathematical expressions. For example, in the equation 3x + 5 = 14, the equal sign separates the numbers 3x + 5 and 14. A mathematical formula may be used to understand the link between the two phrases written on either side of a letter. The logo and the programme are usually interchangeable. As an example, 2x - 4 equals 2.

Because the blueprint is designed on a scale of 12 centimetres Equals 1 metre, each 1 centimetre on the blueprint represents 0.0833 metres (1/12 of a metre).

Assume the triangle chamber on the blueprint has a perimeter of 30 cm. We may apply the following calculation to determine the real perimeter in metres:

Blueprint perimeter x Scale factor x 0.0833 = Real perimeter

Real circumference = 30 x 12 x 0.0833

Actual circumference = 29.988 metres

As a result, the real circumference of the triangle space is around 30 metres.

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The probability are given as follows:

15) P (point is on N.Q.) = 6 / 13

16) P (point is not on Q.R.) = 10 / 13

17) P (point is on N.Q. or RS) = 10/13

18) P  = 1/54

15)

To find the probability that the point is on line segment N.Q., we need to divide the length of N.Q. by the total length of the line segment NS. The length of NS is the sum of the lengths of N.Q., Q.R., and RS, which is 12 + 6 + 8 = 26. Therefore, the probability that the point is on line segment N.Q. is:

P(point is on N.Q.) = length of N.Q. / length of NS = 12 / 26 = 6 / 13

16)

To find the probability that the point is not on line segment Q.R., we need to subtract the length of Q.R. from the length of NS and divide by the length of NS. The length of Q.R. is 6, so the length of NS without Q.R is 12 + 8 = 20. Therefore, the probability that the point is not on line segment Q.R. is:

P (point is not on Q.R.) = (length of NS without Q.R.) / length of NS = 20 / 26 = 10 / 13

17)

To find the probability that the point is on line segment N.Q. or RS, we can add the probabilities of the point being on N.Q. and the point being on RS. We already calculated that the probability of the point being on N.Q. is 6/13. To find the probability of the point being on RS, we can use the same method as in part (15). The length of RS is 8, so the probability that the point is on RS is:

P(point is on RS) = length of RS / length of NS = 8 / 26 = 4 / 13

Therefore, the probability that the point is on N.Q. or RS is:

P(point is on N.Q. or RS) = P (point is on N.Q.) + P(point is on RS) = 6/13 + 4/13

= 10/13

18)

The bus stops at the lot every 18 minutes and stays for 2 minutes, so the shuttle is at the lot for a total of 20 minutes out of every 18 * 60 = 1080 minutes. Therefore, the probability that the bus is at the lot when you arrive is:

P (bus is at the lot) = time the shuttle is at the lot / total time = 20 / 1080

= 1/54

Note that this assumes that you arrive at a random time within the 1080 minutes and that the bus is equally likely to be at the lot at any time during its 20-minute stay.

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Answer:

length of the pan is 10 inches

Step-by-step explanation:

Volume = length x width x height

V = lwh

l = (V) / (wh) = (150 in³) / (7.5 in)(2 in) = 10 in

By conversion formulas, the measures of angles in degrees are, respectively:

In this problem we find thirty cases of angles in radians that must be converted in degrees, this can be done by following conversion formula:

θ' = (180 / π) × θ

Where:

Now we proceed to determine the angles, measured in degrees:

Case 1:

θ' = (29π / 36) × (180 / π)

θ' = 145°

Case 2:

θ' = (17π / 12) × (180 / π)

θ' = 255°

Case 3:

θ' = (8π / 9) × (180 / π)

θ' = 160°

Case 4:

θ' = (55π / 36) × (180 / π)

θ' = 275°

Case 5:

θ' = (5π / 18) × (180 / π)

θ' = 50°

Case 6:

θ' = (53π / 36) × (180 / π)

θ' = 265°

Case 7:

θ' = (2π / 9) × (180 / π)

θ' = 40°

Case 8:

θ' = (47π / 180) × (180 / π)

θ' = 47°

Case 9:

θ' = (π / 180) × (180 / π)

θ' = 1°

Case 10:

θ' = (17π / 45) × (180 / π)

θ' = 68°

Case 11:

θ' = (23π / 90) × (180 / π)

θ' = 46°

Case 12:

θ' = (77π / 30) × (180 / π)

θ' = 462°

Case 13:

θ' = (- 109π / 60) × (180 / π)

θ' = - 327°

Case 14:

θ' = (19π / 30) × (180 / π)

θ' = 114°

Case 15:

θ' = (- 233π / 60) × (180 / π)

θ' = 699°

Case 16:

θ' = (17π / 180) × (180 / π)

θ' = 17°

Case 17:

θ' = (131π / 36) × (180 / π)

θ' = 655°

Case 18:

θ' = (191π / 45) × (180 / π)

θ' = 764°

Case 19:

θ' = (- 71π / 90) × (180 / π)  

θ' = - 142°

Case 20:

θ' = (97π / 30) × (180 / π)

θ' = 582°

Case 21:

θ' = (- 179π / 36) × (180 / π)

θ' = 895°

Case 22:

θ' = (55π / 12) × (180 / π)  

θ' = 825°

Case 23:

θ' = (- 233π / 180) × (180 / π)

θ' = - 233°

Case 24:

θ' = (- 5π / 18) × (180 / π)

θ' = 50°

Case 25:

θ' = (299π / 180) × (180 / π)

θ' = 299°

Case 26:

θ' = (- 269π / 60) × (180 / π)

θ' = 807°

Case 27:

θ' = (- 89π / 30) × (180 / π)  

θ' = 534°

Case 28:

θ' = (47π / 45) × (180 / π)

θ' = 188°

Case 29:

θ' = (91π / 18) × (180 / π)  

θ' = 910°

Case 30:

θ' = (- 107π / 45) × (180 / π)

θ' = - 428°

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The relationship that represent between x, the time in minutes and y, the shot made is y = 4x  .

Proportional relationships are relationships between two variables where their ratios are equivalent. A proportional relationship is one in which two quantities vary directly with each other.

Proportional relationships can be represented as follows;

y = kx

where

Hence, the equation that can be used to represent the relationship between x, the time in minutes and y, the shot made is as follows;

Therefore,

y = kx

where

Therefore,

12 = 3k

k = 12 / 3

k = 4

Therefore,

y = 4x  

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The answer is (B) 1.5 percent.

You can find the growth accounting equation by using:

Growth rate of output equals Technology growth rate plus a* Capital growth rate plus (1-a*Labor growth rate)

Inputting the values provided yields:

5% equals 3% plus (0.8 * Capital Growth Rate) plus (0.2 * 4%).

When we simplify the equation, we obtain:

Capital growth rate equals (5% - 3% - 0.2%) / 0.8, or 1.5%

As a result, the capital growth rate is predicted to be 1.5%.

(B) 1.5 percent is the right answer.

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Answer:

see step by

Step-by-step explanation:

a) the polynomial must be fifth degree, so it must have a [tex]x^5[/tex] term, also need to have 2 additional terms (Lets add any, lets say [tex]x^2+8[/tex] (notice this is totally random, just need to be under 5th degree)

So a polynomial can be

[tex]x^5+x^2+8[/tex]
notice is in standard form since degrees drops from left to right.
Also notice there's an infinite amount of possible answers

b) p-q is the same as -q+p
For example, lets say

[tex]p=x+1[/tex]

[tex]q=3x^2-5[/tex]
[tex]p-q=x+1-(3x^2-5)=x+1-3x^2+5=-3x^2+x+6[/tex]

also

[tex]-q+p=-(3x^2-5)+x+1=-3x^2+5+x+1=-3x^2+x+6[/tex]

notice is the same expression.

The system of linear equations 3y = x + 6 and 6y - 2x = 12 has infinitely many solutions.

Given the system of euqation in the question;

We can solve this system of linear equations using the substitution method:

From the first equation, we can rewrite x in terms of y as:

x = 3y - 6

Substituting this expression for x in the second equation, we get:

6y - 2(3y - 6) = 12

Simplifying this equation, we get:

6y - 6y + 12 = 12

The equation simplifies to 12 = 12.

This means that the two equations are equivalent and represent the same line in the xy-plane.

The system has infinitely many solutions, and all points on the line satisfy both equations.

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Answer:

Graph A

Step-by-step explanation:

As can be seen, the trend in graph A is increasing with each month but not seemingly by as much as graph B;

This is because the scale of the y-axis in graph B has smaller increments;

This creates the impression of a slow increase in sales even though the data in both graphs is actually the same.

Answer: graph A.

appear to increase less.

Step-by-step explanation:

Answer:

(3,-6)

Step-by-step explanation:

Coordinate for the point R is (3, -6)

A polygon with four sides and four vertices is called a quadrilateral. Quadrilateral literally means "four sides" because "quad" means four and "lateral" implies sides. Quadrilaterals come in a variety of sizes, forms, and angles, but they all have four sides in common.

If all of the matching sides and angles of two quadrilaterals are equal in size, they are said to be congruent.

Given that the quadrilateral PQRS congruent to the quadrilateral JKLM.

Find out the all sides and angles of given quadrilateral JKLM and quadrilateral PQRS,

according to the graph the points are:

for quadrilateral JKLM,

J (-6, 2)

K (-3, 5)

L (-5, 8)

M (-8, 4)

for quadrilateral PQRS,

P (9, -7)

Q (6, -4)

R  ( _, _ )

S (7, -9)

By the formula distance between any two points is:

[tex]d=\sqrt{(x_2-x_1)^{2} +(y_2-y_1)^{2}[/tex]    

where, [tex]x_{1}, x_{2} , y_{1}, y_{2}[/tex] are the points of two sides of line.

using that formula we have to find out the points of R is (3, -6)

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Si 25 dólares representan el 15% de una cuenta, podemos usar una regla de tres simple para determinar cuánto hay en total en la cuenta:

15% -----> $25

100% ----> ($25 x 100)/15

100% ----> $166.67

Por lo tanto, hay $166.67 en total en la cuenta.

Answer:

4Step-by-step explanation: